Abstract There are points in the mathematics curriculum where the “rules of the game” change, for example, the meaning and method of multiplication when negative numbers are introduced. At these junctions the new mathematical discourse may be in conflict with learners’ current discourse. Learners may have little intrinsic motivation to accept new rules whose productiveness they cannot yet appreciate, hence, their first steps in the emerging discourse may need to be ritualized - socially motivated by the teacher’s approval. In this article we ask how careful crafting of task situations can support teachers in leading learners into a new discourse. We propose interdiscursivity – the blending of discursive elements from different discourses – as a mechanism for designing task situations to support learners in taking their first steps in an emerging discourse. On the basis of three examples, we suggest that this mechanism may support participation that is intrinsically motivated (explorative).

中文翻译：

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弥合不可通约的话语——对最近发展区教学设计的共同看法

摘要 数学课程中存在一些“游戏规则”发生变化的地方，例如引入负数时乘法的含义和方法。在这些交汇处，新的数学话语可能与学习者当前的话语发生冲突。学习者可能几乎没有内在动机去接受他们还无法欣赏其生产力的新规则，因此，他们在新兴话语中的第一步可能需要仪式化——在教师的认可下具有社会动机。在本文中，我们询问精心设计任务情境如何支持教师引导学习者进入新的话语。我们建议将话语间性——来自不同话语的话语元素混合——作为一种设计任务情境的机制，以支持学习者在新兴话语中迈出第一步。在三个例子的基础上，我们建议这种机制可能支持内在动机（探索性）的参与。